An adaptive policy iteration learning algorithm for optimal tracking control of nonlinear systems with state inequality constraints

This paper proposes a novel policy iteration algorithm to solve the optimal tracking control problem with state inequality constraints. The algorithm aims to optimize the cost function for general nonlinear systems over a specified time horizon. Firstly, the dynamics of the time-varying error system is transformed into an augmented system, thereby facilitating the learning of the system model. Subsequently, concurrent learning is employed to estimate the parameters of the augmented system via instantaneous and historical data. The adaptive policy iteration algorithm is then developed to learn the optimal control strategy. Convergence analysis shows that the algorithm effectively reduces the system's actual tracking cost. Finally, simulations have been conducted to validate the effectiveness of the proposed algorithm.